Monday, 7 January 2013

Magic, markets and models of science

There is a well developed theory that a key impetus for the development of European science in the seventeenth century was magical thinking, developed and promoted through the sixteenth century by the likes of Paracelsus, John Dee and Emperor Rudolph II. While there is little doubt that Hermeticism and Alchemy had a significant influence on the development of natural philosophy, magical thinking cannot explain the uniqueness of the scientific developments in Europe in the 1600s, since magic is a feature of all cultures, notably China. But this factual observation is tempered with an opinion, that good science is open where as magic is hidden and secretive, this is a central theme in Mauss' A General Theory of Magic.

An alternative, minority, theory for the foundations of modern science is in European financial practice. I prefer this theory because, by their very nature markets are social, collaborative, open, forums (those queasy about markets might wish to consider my view). Evidence for the significance of financial practice in the development of science comes in the fact that Copernicus was trained in financial mathematics and wrote on money before he wrote on cosmology, the Merchant Adventurer Thomas Gresham was a more influential contemporary of Dee, despite relative number of contemporary biographies of the two Elizabethians, who laid the basis of the Royal Society with the establishment of Gresham College. Simon Stevin was trained in finance and founded the influential Dutch Mathematical School that inspired Descartes and performed many of the experiments that Galileo is famous for. While Newton's interest in magic has been promoted, the fact that he spent half his life running the Mint is often overlooked.

Furthermore, magic was most influential in central Europe, centred on Rudolph's court, while the scientific revolution was centred in western Europe, by the likes of Huygens and Bernoulli who were as likely to work on financial problems as physical ones. Finally, my observation of good financial practitioners is that, contrary to popular belief, they do not believe they can control the markets, rather they have to navigate through its intrinsic uncertainties using the best tools available - specifically mathematics. This contrasts with the image of the magician controlling nature.

To develop this point, there has been significant criticism of the use of mathematics in the the lead upto the Credit Crisis, that is still affecting all our lives. In particular, the use of a technique known as Value at Risk, to measure the riskiness of investments and the Gaussian Copula, the "formula that killed Wall Street". Now, the fact is that both these techniques emerged out of the investment bank, J.P. Morgan, and the problem in blaming these mathematical techniques for the Credit Crisis is that J.P. Morgan did not engage in trading Credit Default Swaps on Mortgage Backed Securities, and did not hold the alchemical Collatorallised Debt Obligations of Mortgage Backed Securities. The reason? J.P. Morgan having developed the techniques understood them and could not reconcile the model results with their "opinions" of the market. The "science" was being tempered by "opinion" (all this is covered in Gillian Tett's book Fool's Gold, or STS/HPS types might like this).

While, at first sight, these observations might not seem relevant to my criticism of the article by Cox&Ince, I see the two as being linked. Fundamentally, my concern, and it might be unjustified, is that in advocating the primacy of "science" people are endorsing a kind of group think that leads to the sorts of disasters like the Credit Crisis. This might be seen as a bit melodramatic but lets consider two examples, climate change and evolution.

My understanding is that there is little academic dispute about most of the raw data relating to the current climate (modulo the hockey-stick): temperatures are rising and there has been an increase in CO2 in the atmosphere. The academic debate is to what extent man-made emissions of CO2 are causing the rise in temperature, and this is a question of model choice, and since models are made by humans they are, unfortunately for Cox&Ince, social constructs. In November I listened with interest to Andy Kerr talk about plans to bring academics on both sides of the climate debate to discuss the model issues in order to move to a better consensus. This is good science, but the science is not changing as a consequence of new data but as a consequence of human deliberation.

The other great bug-bear of science is evolution. As a mathematician I admire Alan Turing, Turing's most significant work (in terms of citations and impact), undertaken whilst at Manchester at the time of his suicide, was on morphogenisis and this was inspired by Sir D'Arcy Wentworth Thompson'sOn Growth and Form, written to counterbalance the dominance of Darwinian evolution and the emphasis on survival of the fittest. Biological structuralists have come under attack from neo-Darwinists for introducing metaphysical (i.e. mathematical) explanations for phenomena. Who is being un-scientific here, the mathematicians or the neo-Darwinists?

Paul Nurse, the President of the Royal Society whom Jack Stilgoe has associated with Cox&Ince, has argued that "keep science as far as is possible from political, ideological and religious influence". I think Nurse is mistaken here for two reasons.

Firstly, in the thirteenth century the Dominicans, such as Thomas Aquinas and Albert the Great, began Europe's development of science by developing the idea that God could not interfere with nature at will: the deity designed the cosmos, like a machine, but once set in motion they could not interfere with it. The Franciscans, such as John Duns Scotus and William of Ockham, took a different view: God was not constrained by nature. Of course today only a fool would agree with Scotus and Ockham. Or would they? The idea of a Black Swan was developed at this time, the empirical rationalist Dominicans argued that, since no Black Swan had been observed they were not possible. The fideist Fransciscans disagreed, God (and nature) could be capricious and produce a Black Swan if they wanted to, and of course they did. (The Black Swan of Nassim Taleb is different, it is a rare event and in finance we would call Taleb's swan an epistemological problem, Scotus' an ontological problem, and yes finance practitioners are talking in these terms).

The point is, understanding the theological arguments about Black Swans help in our understanding of the contemporary debate. A good scientist, in my view, needs to be humble and accept that they do not, and cannot, know everything. This was central to good financial practice, until "science" became influential through economics, physics and biology.

This leads me on to the second reason why I think Paul Nurse is wrong, by separating themselves from outside influences scientists as susceptible to loosing their humility, or at least of becoming trapped in an ivory tower. This is precisely what happened in finance at those inbstutions that failed, unlike J.P. Morgan. I am of the opinion that the consequences for society could be as dire if science is not integrated with political, ideological and religious influences. Argument should be suppressed if you think you'll lose the argument, but is benign otherwise, something I have discovered as a parent.

Cox&Ince begin their article by describing the significant improvements in the human condition over the past two to three hundred years, which they ascribe to the "scientific method". This brash statement cannot, scientifically, be offered as fact. As a counter example I offer the case of the Soviet Union/Russia. Few would argue that Russia's scientific achievements between 1950 and 2010 were not comparable to those of the UK, France or Germany, but these achievements have not resulted in the quality of life and freedoms enjoyed by western Europeans. Indeed there are many western nations that cannot match Russia's scientific achievement yet are none the less more attractive places to live, Belgium for example.

The argument that science leads to wealth is an opinion not supported by fact, an argument originating in Thomas Gresham's less successful, but more famous, nephew, Francis Bacon. Good science is a consequence of good political structures, and good political structures are closely associated with sound financial practice, and without these social structures there would not have been the technological advances that we enjoy today. This is why I choose Athena as my avatar, acknowledging the precedence of the civilising god over the technological god, Hephaestus. Sorry, am I mixing religion and science here?

Promoting the view that scientists hold a particularly important position in the context of political decision making is dangerous, because despite their best intentions scientists are frequently wrong and are rarely able to distinguish what is true from what is false (the issue about the failure of the Law of Excluded Middle in my last post). A technocracy is just as much an oligarchy as a monarchy, theocracy, plutocracy or stratocracy and is as likely to kill the goose that lays the golden egg as any other system of government that denies dissent.

A historical example of scientists being wrong. Galileo was convicted by the Catholic Inquisition for publishing Dialogue Concerning the Two Chief World Systems in 1632. Galileo's original title for the Dialogue was Dialogue on the Ebb and Flow of the Sea, because, as a consequence of the Copernican theory and mathematics, Galileo argued that there would be one tide a day. When he sent the book to the Church for approval, he was told to change the title because every European sailor knew that there were two tides a day. For the Church of the time, built on Aristotle, Galileo's use of mathematics to describe reality was not just philosophically wrong, it also resulted in absurd conclusions. The historian, Harold Brown explains

Galileo's attempt to account for the tides as a result of the combined daily and annual motion of the earth, and his belief that this argument provided a physical proof that the earth moves, stands as something of an embarrassment.

Are we to consign Galileo to the set of non-scientists and commend the Church for his prosecution, I doubt this would go down well with the likes of Cox&Ince.

The point is scientists must "commit to an evaluative framework", this is what Galileo has done, nailing his colours to mathematics and the Copernican model. The phrase "commit to an evaluative framework" comes out of one of the rare scientific studies of the behaviour of traders, by Daniel Beunza and David Stark, who note that

the trader is emotionally distant from any particular trade, to be able to take a position, the trader must be strongly attached to an evaluative principle and its affiliated instruments

This description of a trader seems to fit that of a scientist. However, what is understood in finance, for example the traders at J.P. Morgan using VaR and the Gaussian Copula, and was understood by Duns Scotus and Ockham, is that faith in the evaluative framework should not be blind, the scientist must be open to persuasion that they may be wrong. The view taken by Cox and Ince is that this can only occur after new data has appeared, but the vacuousness of this position is given by the example of the Black Swan and the way that science can avoid these lapses in prudence is by being open.

It might seem to be splitting hairs to argue in favour of science originating out of finance rather than magic, but I am of the opinion that creation myths have a critical role in how cultures view themselves. If science believes it emerges out of magic it will be forever associated with secret knowledge that enables the magician to control nature and convert base metal into gold. If we regard science as originating out of markets constructed social instruments, then it is natural that we think of science as being "just another" social construction and it is made more human, and possibly more relevant. Simultaneously, and this is my ultimate objective, we shall start observing markets from a scientific perspective, rather than having them hidden from public oversight by a veil of mystery and obscure incantations.

Now if I have been a bit obtuse, let me be more explicit. I worry about the views around the belief that "science" has a special status that makes it difficult to challenge was a contributory factor in the Credit Crisis. I will give an anecdote that a physical scientist would dismiss but social scientists would consider as evidence. After the collapse of British and American banks there was anger in the British and American banking community that the French had been engaged in exactly the same practices as the failed Anglo-Saxon banks, but had weathered the storm. I was party to a private conversation where a prominent mathematician who works for a prestigious French bank was asked about this complaint. The continentally trained mathematician pointed out that "we thought the models were probably wrong before the Crisis, we knew they were wrong during the Crisis, the view was the solvency of the bank should not be compromised on the basis of bad models". The UK/US banks can be seen as believing in the models before and during the Crisis, as a result, Lehmans, Bear Sterns BoS, Northern Rock and RBS no longer exist as independent entities where as Paribas and SocGen do. In a way, this aspect of the Credit Crisis can be seen as empirical evidence for a failure of Analytic Philosophy and a triumph for Continental Philosophy.

Despite the fact that I have spent an hour or so writing this piece, and you have spent time reading it, I do not think we should worry too much about the article by Cox&Ince. Neither of the authors is qualified to inform policy makers, and I suspect the likes of Andy Kerr advising on climate change, the scientists advising DEFRA on GMOs or the badger cull, or even my modest contribution to DECC's modelling efforts, believe that policy makers should be so confident of accepting scientific advice without it being tempered by political considerations. Cox & Ince, perhaps, should focus more on the distinction between science and entertainment rather than the relationship between science and politics.

3 comments:

" In a way, this aspect of the Credit Crisis can be seen as empirical evidence for a failure of Analytic Philosophy and a triumph for Continental Philosophy."

But logical positivism, a crucial part of analytic philosophy, was developed by the Vienna Circle, right?

It appears that the contradiction is inherent in the "Continent".

AS far as magic and science, the relationship is clear and was explained by newton: science explains cause after cause after cause until it reaches a final cause, which is magical. Everything in between is science:

"Whereas the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical;", Sir I. Newton.

Good read, hard to follow at times. Maybe, if I may, the reader will be helped to follow your thinking if there was a summeary that makes your position clear at the start as related to the problem. I hope this is not taken as an advice but only as a humble request.

An interesting idea on the emergence of science. A developmental neurobiological perspective (organism and species) resolves your question. So-called 'magical thinking' is an expression of the various associative processes of System 1, while an ability at maths is definitely System 2. (See D. Kahneman, "Thinking, Fast and Slow" on 'dual process theory.') Kahneman and his behavioral economic colleagues have amply shown our grasp on System 2 thinking is tenuous at best. That some so-called 'thoughtful people' would mistake one for the other and then defend it is to be expected.

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.